This post explains how methods from ordinal analysis can be used to prove results in reverse mathematics. It may be surprising that this is possible, given that the traditional aims of the two areas are somewhat different: reverse mathematics proves implications between different statements about infinite sets, while ordinal analysis eliminates the infinite from proofs…
Anton Freund
I am a postdoc of Ulrich Kohlenbach in the Logic Group at TU Darmstadt. Before, I was a PhD student of Michael Rathjen at the University of Leeds.
My research is concerned with the foundations of mathematics, especially the metamathematics of arithmetic (first and higher order, reverse mathematics) and weak set theories. I am particularly interested in connections between the abstract (uncountable, non-computable and higher type objects) and the concrete (computable and continuous objects, computational content of proofs, mathematical independence results). I specialize in proof theory (ordinal analysis, dilators), but also enjoy using methods from other areas, in particular from set theory.
